Title :
A Primer on Stochastic Differential Geometry for Signal Processing
Author :
Manton, Jonathan H.
Author_Institution :
Dept. of Electr. & Electron. Eng., Univ. of Melbourne, Melbourne, VIC, Australia
Abstract :
This primer explains how continuous-time stochastic processes (precisely, Brownian motion and other Itô diffusions) can be defined and studied on manifolds. No knowledge is assumed of either differential geometry or continuous-time processes. The arguably dry approach is avoided of first introducing differential geometry and only then introducing stochastic processes; both areas are motivated and developed jointly.
Keywords :
continuous time systems; differential geometry; signal processing; stochastic processes; Brownian motion; Ito diffusion; continuous-time stochastic process; signal processing; stochastic differential geometry; Differential equations; Linear approximation; Manifolds; Random variables; Stochastic processes; Vectors; Brownian motion; Differential geometry; Itô diffusions; Lie groups; continuous-time stochastic processes; estimation theory on manifolds; stochastic differential equations on manifolds;
Journal_Title :
Selected Topics in Signal Processing, IEEE Journal of
DOI :
10.1109/JSTSP.2013.2264798